Placing rock under ladder to stop it from slipping

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The discussion revolves around understanding the solutions to two parts of a problem regarding a ladder's stability. Participants express confusion about deriving the answer of 5.77 cm for part (a) using part (b) and seek clarification on the methodology. The use of similar triangles is emphasized as a key concept to explain the relationship between the ladder's angles and dimensions. A suggestion is made to draw a diagram to visualize the problem better, which could aid in grasping the solution. Overall, the conversation highlights the importance of visual aids and foundational geometry in solving the problem.
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Homework Statement
Please see below
Relevant Equations
Please see below
For part(a) and (b),
1675394717684.png

The solution is,
1675394798329.png

Can someone please explain the solutions to (a) and (b) to me? I don't understand where they got 5.77 cm from.

Many thanks!
 
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They used b to get a.

What answer did you get ?
 
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hmmm27 said:
They used b to get a.

What answer did you get ?
Thanks for your reply @hmmm27 ! The got 5.77 cm. But don't you think that is a little strange using (b) to get (a)?

I still don't understand (b). Many thanks!
 
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So, what answer did you get ? and how did you arrive at it.
 
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hmmm27 said:
So, what answer did you get ? and how did you arrive at it.
I did't get an answer @hmmm27. I am wondering how the solutions arrived at their anwser.
 
Callumnc1 said:
is a little strange using (b) to get (a)?
Not at all. The answer to part b) is the explanation of how they arrived at the solution to a). Presumably this uses ideas earlier in the chapter, but I do not have the book.
Draw a diagram showing the ladder in both positions. Label the right-hand foot of the ladder P (the pivot point), the right-hand top of the tilted ladder B, the right-hand top of the upright ladder B', the left-hand bottom of the tilted ladder A, the left-hand bottom of the upright ladder A'.
Drop a vertical from A' to meet the sloping ground.
Draw a horizontal from B to meet PB'.
Spot similar triangles.
 
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haruspex said:
Not at all. The answer to part b) is the explanation of how they arrived at the solution to a). Presumably this uses ideas earlier in the chapter, but I do not have the book.
Draw a diagram showing the ladder in both positions. Label the right-hand foot of the ladder P (the pivot point), the right-hand top of the tilted ladder B, the right-hand top of the upright ladder B', the left-hand bottom of the tilted ladder A, the left-hand bottom of the upright ladder A'.
Drop a vertical from A' to meet the sloping ground.
Draw a horizontal from B to meet PB'.
Spot similar triangles.
Thank you @haruspex , I will try that!
 
Callumnc1 said:
Can someone please explain the solutions to (a) and (b) to me? I don't understand where they got 5.77 cm from.

Many thanks!
I don’t see a reason for translating tilting into angle and back to vertical displacement of the left leg.
Are you familiar with similar triangles?

https://www.mathsisfun.com/geometry/triangles-similar.html

If so, I would draw a 0.41 x 0.41 square at the bottom of the rectangle formed by the ladder dimensions.
The horizontal displacement of the top corners of that square should be equal to the vertical one, and both should be proportional to the horizontal displacement of the top of the ladder.
 
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Lnewqban said:
I don’t see a reason for translating tilting into angle and back to vertical displacement of the left leg.
Are you familiar with similar triangles?

https://www.mathsisfun.com/geometry/triangles-similar.html

If so, I would draw a 0.41 x 0.41 square at the bottom of the rectangle formed by the ladder dimensions.
The horizontal displacement of the top corners of that square should be equal to the vertical one, and both should be proportional to the horizontal displacement of the top of the ladder.
Thank you for your reply @Lnewqban ! Yeah I'm familiar with similar triangles.
 
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Callumnc1 said:
Thank you for your reply @Lnewqban ! Yeah I'm familiar with similar triangles.
You are welcome. :smile:
Then, you now understand where they got 5.77 cm from.

We have two triangles that are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Please, see scaled drawing representing our problematic ladder.
 

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Lnewqban said:
You are welcome. :smile:
Then, you now understand where they got 5.77 cm from.

We have two triangles that are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Please, see scaled drawing representing our problematic ladder.
That is very helpful @Lnewqban ! Thank you for your help!
 
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